Related papers: Exponential Quantum Speed-ups are Generic
Variational quantum algorithms dominate contemporary gate-based quantum enhanced optimisation, eigenvalue estimation and machine learning. Here we establish the quantum computational universality of variational quantum computation by…
Executing quantum circuits on currently available quantum computers requires compiling them to a representation that conforms to all restrictions imposed by the targeted architecture. Due to the limited connectivity of the devices' physical…
We study possible advantages of randomized and quantum computing over deterministic computing for scalar initial-value problems for ordinary differential equations of order k. For systems of equations of the first order this question has…
(Abridged.) Quantum computers promise to solve some problems exponentially faster than traditional computers, but we still do not fully understand why this is the case. While the most studied model of quantum computation uses qubits, which…
This paper initiates the study of quantum algorithms for matroid property problems. It is shown that quadratic quantum speedup is possible for the calculation problem of finding the girth or the number of circuits (bases, flats,…
We propose a scheme for translating metrological precision bounds into lower bounds on query complexity of quantum search algorithms. Within the scheme the link between quadratic performance enhancement in idealized quantum metrological and…
Quantum computations are typically compiled into a circuit of basic quantum gates. Just like for classical circuits, a quantum compiler should optimize the quantum circuit, e.g. by minimizing the number of required gates. Optimizing quantum…
We give new evidence that quantum circuits are substantially more powerful than classical circuits. We show, relative to a random oracle, that polynomial-size quantum circuits can sample distributions that subexponential-size classical…
Although quantum circuits have been ubiquitous for decades in quantum computing, the first complete equational theory for quantum circuits has only recently been introduced. Completeness guarantees that any true equation on quantum circuits…
Quantum algorithms could efficiently solve certain classically intractable problems by exploiting quantum parallelism. To date, whether the quantum entanglement is useful or not for quantum computing is still a question of debate. Here, we…
Quantum algorithms are known for presenting more efficient solutions to certain computational tasks than any corresponding classical algorithm. It has been thought that the origin of the power of quantum computation has its roots in…
Quantum computing (QC) offers a new computing paradigm that has the potential to provide significant speedups over classical computing. Each additional qubit doubles the size of the computational state space available to a quantum…
Quantum amplitude amplification and estimation have shown quadratic speedups to unstructured search and estimation tasks. We show that a coherent combination of these quantum algorithms also provides a quadratic speedup to calculating the…
We construct a classical algorithm that designs quantum circuits for algorithmic quantum simulation of arbitrary qudit channels on fault-tolerant quantum computers within a pre-specified error tolerance with respect to diamond-norm…
State-of-the-art classical optimization solvers set a high bar for quantum computers to deliver utility in this domain. Here, we introduce a quantum preconditioning approach based on the quantum approximate optimization algorithm. It…
A central challenge in quantum computing is to identify more computational problems for which utilization of quantum resources can offer significant speedup. Here, we propose a hybrid quantum-classical scheme to tackle the quantum optimal…
Recent technological developments have focused the interest of the quantum computing community on investigating how near-term devices could outperform classical computers for practical applications. A central question that remains open is…
Quantum algorithms can potentially solve a handful of problems more efficiently than their classical counterparts. In that context, it has been discussed that Markov chains problems could be solved significantly faster using quantum…
We present a quantum algorithm for simulating the classical dynamics of $2^n$ coupled oscillators (e.g., $2^n$ masses coupled by springs). Our approach leverages a mapping between the Schr\"odinger equation and Newton's equation for…
Quantum algorithms require less operations than classical algorithms. The exact reason of this has not been pinpointed until now. Our explanation is that quantum algorithms know in advance 50% of the solution of the problem they will find…